Convergence and Stability of Locally R -invariant Solutions of Ricci Flow
نویسنده
چکیده
Valuable models for immortal solutions of Ricci ow that collapse with bounded curvature come from locally G-invariant solutions on bundles GN ,! M !Bn, with G a nilpotent Lie group. In this paper, we establish convergence and asymptotic stability, modulo smooth nite-dimensional center manifolds, of certain RN -invariant model solutions. In case N + n = 3, our results are relevant to work of Lott classifying the asymptotic behavior of all 3-dimensional Ricci ow solutions whose sectional curvatures and diameters are respectively O(t 1) and O(t1=2) as t!1.
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